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Table of Content
30 June 2024, Volume 39 Issue 2
Previous Issue
Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity
JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei
2024, 39(2): 111-127. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.001
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In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by
Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of
solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we
prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.
Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge
PANG Ru-yi, CHEN Qiao-ling
2024, 39(2): 128-143. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.002
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In this paper, a discrete predator-prey model with prey refuge is investigated.
It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and
1:3 resonances. The bifurcation diagrams and phase portraits show that the model has
some interesting complex dynamical behaviors, such as limit cycle, periodic solutions,
chaos and codimension-1 bifurcations.
Sure Independence Screening via Semiparameteric Copula Learning
XIN Xin, XIE Bo-yi, LIU Ke-ke
2024, 39(2): 144-160. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.003
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This paper is concerned with ultrahigh dimensional data analysis, which has
become increasingly important in diverse scientific fields. We develop a sure independence
screening procedure via the measure of conditional mean dependence based on Copula
(CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence
screening procedures which respectively based on the Pearson correlation, conditional
mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly
improve the performance of feature screening. We establish the sure screening property for
the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical
comparison indicates that the CC-SIS performs better than the other two methods in
various models. At last, we also illustrate the CC-SIS through a real data example.
Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs
XI Wei-ge, XU Tao
2024, 39(2): 161-170. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.004
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Let D be a weighted digraph with n vertices in which each arc has been
assigned a positive number. Let A(D) be the adjacency matrix of D and W(D) =
diag(w
1
+
,w
2
+
,...,w
n
+
). In this paper, we study the matrix A
α
(D), which is defined as
A
α
(D) =αW(D)+ (1−α)A(D), 0≤α≤1.
The spectral radius of Aα(D) is called the Aα spectral radius of D, denoted by λα(D).
We obtain some upper bounds on the Aα spectral radius of strongly connected irregular
weighted digraphs.
Strong Convergence Rates of Reiterated Homogenization Problems
ZHAO Jie, WU Xi-min, WANG Juan
2024, 39(2): 171-179. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.005
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In this paper, we study the reiterated homogenization operators L
ε
=
−div(A(x/ε,x/ε2
)∇). We establish the homogenized problem and representation equation by introducing the two correctors. As a consequence, we obtain the H
0
1
and L
2
convergence estimates of solutions.
The Gauss-Bonnet Formula of a Conical Metric on a Compact Riemann Surface
FANG Han-bing, XU Bin, YANG Bai-rui
2024, 39(2): 180-184. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.006
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We prove a generalization of the classical Gauss-Bonnet formula for a conical
metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue
integrable with respect to the area form of the metric. We also construct explicitly some
conical metrics whose curvature is not integrable.
On Minkowski Constants of Bouw-M¨oller Surfaces
XU Yun-long, ZHONG Yu-min
2024, 39(2): 185-199. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.007
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We consider the Bouw-M¨oller surfaces with two parameters m,n when they
are not both even or m=n, n is even. We computer the e-Minkowski constant of them.
Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br#
GUAN Daniel, LIANG Meng-xiang
2024, 39(2): 200-220. doi:
10.13371/j.cnki.chin.q.j.m.2024.02.008
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In this paper, we revisit the K
¨ahler structures on the affine quadrics M
1
={z
1
2
+z
2
2
+z
3
2
= 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen.
